Stimulating an immune response against cancer through adoptive transfer of tumor-targeting lymphocytes has shown great promise in hematological malignancies, but clinical efficacy against many common solid epithelial cancers remains low. Targeting 'neoantigens'-the somatic mutations expressed only by tumor cells-might enable tumor destruction without causing undue damage to vital healthy tissues. Major challenges to targeting neoantigens with T cells include heterogeneity and variability in antigen processing and presentation of targets by tumors, and an incomplete understanding of which T cell qualities are essential for clinically effective therapies. Finally, the prospect of targeting somatic tumor mutations to promote T cell destruction of cancer must contend with the biology that not all tumor-expressed 'neoepitopes' actually generate neoantigens that can be functionally recognized and provoke an effective immune response. In this Review, we discuss the promise, progress and challenges for improving neoantigen-targeted T cell-based immunotherapies for cancer.